# Questions tagged [wolfram-alpha]

For mathematical questions related to the usage of WolframAlpha.

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### Solve basic system of equations with two unknowns. Why solution doesn't exists?

The following equation has no solution, but I'm not sure why exactly: $7 = 3x_1 + 5x_2 \\ 13 = (1 - x_1)3 + (1 - x_2)5 + 21$ Code for Wolfram Alpha ...
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### Restricting Domain in Wolfram Alpha for Nested Quantifiers

Is there a way to restrict the domain to all positive integers when you're using Resolve[] on nested quantifiers in Wolfram Alpha? If so, how? If not but there is ...
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### How do I find $\frac{\mathrm{d}}{\mathrm{d}x} \int_{x}^{\infty} f(t, x) \mathrm{d} t$?

I am trying to compute the following derivative: $$\frac{\mathrm{d}\Big(\int_{x}^{\infty} f(t, x) \mathrm{d} t\Big)}{\mathrm{d}x} \text{.}\tag{1}$$ It is straightforward to compute the following ...
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### Wolfram Alpha computation of exponents

I am a bit confused by a Wolfram Alpha. In my calculations I had a term like $x^{(3/2)}$ which I wrote as $\sqrt{x^3}$. As silly mistakes happen quite often to me, I often double check stuff like this ...
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### How to solve this system of equations in Wolfram Alpha?

I want to solve P0 + t0 * V0 + t2 * V2 == P1 + t1 * V1 for t0, t1 and t2, which are scalars, whereas the uppercase variables ...
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### Can someone explain me what the limes of this example is? What does this solution of Wolfram mean?

This is the example I tried to solve with WolframAlpha. The result is also in the picture. Can someone explain me what the limes of this example is and how can i get there by hand? Limit[Power[(40)...
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### Why is Wolfram's (presumably more precise) Maclaurin series a much worse approximation than my own (presumably less precise) series?

I recently answered this question, concerning the existence and nature of the implicit function defined by: $$F(x,y)=x^3-y^3-3xy+1$$ For $x$ close to $0$ - roughly the range $|x|\lt0.4$ - I showed how ...
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Consider the following limit $$\lim_{x\to-\infty}x-\sqrt{x^2+7x}$$ Going through some algebra leads to \begin{align} \lim_{x\to-\infty}x-\sqrt{x^2+7x}&=\lim_{x\to-\infty}\frac{(x-\sqrt{x^2+7x})... 0 votes 2 answers 55 views ### Why does WolframAlpha give me an ugly graph for the input "(cos x-1)/x^2 when x=0.01"? The function \dfrac{\cos x-1}{x^2} is differentiable everywhere except for x=0. However, when I give WolframAlpha the input "(cos x-1)/x^2 when x=0.01", it gives me an ugly graph as ... 0 votes 2 answers 160 views ### Graphing parametric equation software? Desmos/Mathematica/ other math software? I want to view what the graph of, for example, x=\sin t,\quad y = \sin(10t) looks like, but not as a static graph \ y=f(x),\  but rather one where we can see the movement of the point on the \ x-... 0 votes 1 answer 74 views ### Why does Wolfram Alpha give different answers to this algebraic equation depending on how it is entered? I am trying to solve the equation Ce^{-\sqrt L t} + De^{\sqrt L t} = Ce^{-\sqrt L (t + 2m\pi)} + De^{\sqrt L (t + 2m\pi)} for L. Here Wolfram Alpha returns the solution m = \frac{in}{\sqrt L}, ... 3 votes 2 answers 174 views ### Wolfram and Matlab show different Fourier Transforms for the function H(z)=\sqrt{\frac{2}{\pi z}}e^{i\left(z-\frac{\pi}{4}\right)} I'm struggling with a discrepancy that Wolfram and Maple are giving me. To make everything comprehensible, I describe in the following what I did step by step. When I let Wolfram calculate the Fourier ... 1 vote 2 answers 101 views ### How to calculate the result of a recursive equation? I'm looking for a tool (like Wolfram Alpha) that can calculate the result of  B(P,N)  Where B(P,N) is a recursive function defined as follows:  \left\{\begin{matrix} B(P,N)=\frac{-(-1)^{\frac{N}... 1 vote 2 answers 234 views ### Computing local and global minima on Wolfram Alpha Consider \sqrt{x^2+y^2}+2\sqrt{x^2+y^2-2x+1}+\sqrt{x^2+y^2-6x-8y+25}. I need to find global or local minima of this function, but Wolfram Alpha doesn't seem to find one; the answer is that 1 + 2\... 1 vote 3 answers 100 views ### e^{0\times I} in Wolfram Alpha broken? How comes that e^{0_2} = e^{\begin{pmatrix}0 & 0 \\ 0 & 0\end{pmatrix}} = \begin{pmatrix}1 & 1 \\ 1 & 1\end{pmatrix} = 1_2 $$according to Wolfram Alpha? Shouldn't e to the power ... 1 vote 2 answers 41 views ### Quartic Circulant graph notation example I would like to ask. I found the original image from Wolfram website and then cropped this example of circulant graph. Source: https://mathworld.wolfram.com/QuarticGraph.html Why does it says it is ... 0 votes 0 answers 121 views ### Wolfram alpha gives incorrect inverse function I have trouble with Wolfram Alpha not fully calculating inverse of higher-order polynomial function. Function$$f(x)=3 x^6-5 x^4-4 x^2+8$$(graph presented on a first photo Graph of f(x)) is not a ... 5 votes 2 answers 250 views ### Matrix exponential weirdness in WolframAlpha - it fails on diagonal matrices? So Wikipedia says this, which makes sense: But Wolfram computed this: Is this a bug or am I just extremely tired? 4 votes 1 answer 141 views ### What is the value of \textstyle{{\sum\limits_{n=1}^{\infty}{\lim\limits_{u\rightarrow\infty}{\frac{(-1)^nu^{n+s}}{(n-1)!(n+s)}}}}}? First, I had put \textstyle{\displaystyle{\sum_{n=1}^{\infty}{\lim_{u\rightarrow\infty}{\frac{(-1)^nu^{n+s}}{(n-1)!(n+s)}}}}} into wolfram alpha and got nothing. Then, I thought about inter-changing ... 0 votes 0 answers 281 views ### Why does Wolfram Alpha get this binomial coefficient sum wrong? The sum I want to evaluate is \sum_{i=2}^m \binom{p-1}{i-2} * \binom{n-k}{m-i}. Here we have p<k<=n and m<=n, all positive integers; I don't know how to communicate that to Wolfram ... 0 votes 0 answers 37 views ### Define start and stop for recursive formula A recursive formula like a_{n} = a_{n-1}+4, how is it specified where to start and stop? In any computer language, I'd write something ... 0 votes 1 answer 204 views ### Wolfram alpha plot of a piecewise function with 2 domains. [closed] So, Wolfram Alpha is capable of plotting two functions in one figure. But I am trying to express a piecewise function that has a different form on two (touching) domains. In C code: ... 2 votes 2 answers 106 views ### Is \frac{x^3}{x^2+y^4} continuous at (0,0)? In an exam I was asked to determine if a function f:\mathbb R^2\to \mathbb R is continuous at a point (x_0,y_0), I needed to check if$$\lim_{(x,y) \to (x_0,y_0)} f(x,y) = f(x_0,y_0)$$We consider ... 0 votes 0 answers 128 views ### Specify choice variables and constants in Wolfram Alpha for maximisation I seek to use Wolfram Alpha for some constrained optimisation problems, but I am unable to "tell" Wolfram Alpha, which of the symbols are variables (which ought to be chosen to maximise the ... 3 votes 1 answer 54 views ### F(x,y)=(x^2,y) is not differentiable (According to WA), what am I missing? Either wolfram alpha is getting crazy or I just completely misunderstood differentiability. Shouldn't it be enough for the partial derivatives to exist and to be continuous? Would the differential not ... 1 vote 1 answer 58 views ### Is the inequality \sqrt{(2^r + 1)(t + 1)} \leq \min(2^r, t) false in general? My question here is pretty basic: Is the inequality \sqrt{(2^r + 1)(t + 1)} \leq \min(2^r, t) false in general? I tried asking WolframAlpha for its solutions, it says that no solutions exist. I ... 1 vote 4 answers 131 views ### \lim_{z\to1}\frac{1-z^*}{1-z} using Wolfram Alpha I wanted to verify the answer to many questions on limits of complex numbers. So, I tried using Wolfram Alpha for the same.$$\lim_{z\to1}\frac{1-z^*}{1-z}$$does not exist. [using path y=m(1-x)] ... 0 votes 0 answers 17 views ### How to plot a skewed randon numbers on Wolfram Alpha, basically non-linear Ox axis? I want to see Gauss' bell, but drawn over non-linear Ox axis. Basically i want to visually "catch" some asymetric and very rough plot, that hopefully is just a transformed normal ... 0 votes 0 answers 29 views ### Can Wolframalpha.com display the image of the map (x,y,z) \rightarrow (x^{2}y,x-z)? I can do functions, like f(x,y,z) = 1. But is it possible to show the image of this morphism too; (x,y,z) \rightarrow (x^{2}y,x-z)? 2 votes 1 answer 85 views ### Maximise (\cos x\ln (x^{\frac1x})-\frac{\cos x\log_{10}x}{\ln(\ln x)})^{\cos x} Maximise$$\large \left(\cos x\ln (x^{\frac1x})-\frac{\cos x\log_{10}x}{\ln(\ln x)}\right)^{\cos x}$$I wonder why Mathematica says infinity as answer, but on desmos graph it is clear that it is less ... 0 votes 1 answer 83 views ### Third vertex of equilateral SPHERICAL triangle I’m trying to solve Fermat’s problem on sphere for the given triangle ABC using wolfram.I already made out,that in order to find a Fermat’s point i need to build three equilateral triangles on each ... 0 votes 0 answers 29 views ### Discrepancy in Wolfram Alpha for the domain of (\log{x})^{-e^x} In my question Question I have discussed in the comments of the domain of$$(\log{x})^{-e^x}$$In wolfram alpha as matter of fact the domain is x\geq 1, but I am not convinced of this fact since ... 0 votes 1 answer 28 views ### Is it possible to use imaginary guesses with secant method? I was playing with Wolfram Alpha today, and noticed that while I could use, say, 2i as a guess to solve e^x+2=0 with the help of Newton's method, I couldn't do the same with the secant method. Is ... 1 vote 1 answer 135 views ### Does every Matrix have a REF? I'm wondering if anyone here has experience using Wolframalpha? I can't seem to get a row echelon form (REF) or echelon form, it always does reduced row echelon form (R-REF). Anybody know how to get ... 2 votes 1 answer 114 views ### How does WolframAlpha calculate the power of 10 representation of a number? [closed] Whenever I type some crazy big number on WolframAlpha, it outputs its power of 10 representation. For example, if I input$$ \large e^{6^{3643.23976}}$$it outputs$$ \large 10^{10^{2834.629359002706}}...
When plotting the function $$\frac{(x^2 -1)}{(x^2 -x -2)}$$ with Wolfram alpha, the second plot has a slant "equals" sign right below when the graph hits the y-axis. What does this indicate? ...